| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 25601 |
\begin{align*}
12 x^{3} y+24 y^{2} x^{2}+\left (9 x^{4}+32 x^{3} y+4 y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
78.931 |
|
| 25602 |
\begin{align*}
y y^{\prime \prime }+a {y^{\prime }}^{2}+b y^{2} y^{\prime }+c y^{4}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
78.965 |
|
| 25603 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }+y^{2}&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
79.006 |
|
| 25604 |
\begin{align*}
x \left (x -2 y\right ) y^{\prime }+y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
79.026 |
|
| 25605 |
\begin{align*}
y^{\prime }&=\frac {x}{y+\sqrt {x^{2}+1}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
79.043 |
|
| 25606 |
\begin{align*}
y y^{\prime \prime }-{y^{\prime }}^{2}-\left (a y-1\right ) y^{\prime }+2 y^{2} a^{2}-2 b^{2} y^{3}+a y&=0 \\
\end{align*} |
✗ |
✗ |
✓ |
✗ |
79.589 |
|
| 25607 |
\begin{align*}
y^{\prime \prime }&=\frac {1}{y}-\frac {x y^{\prime }}{y^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
79.609 |
|
| 25608 |
\begin{align*}
4 x^{2} y^{\prime \prime }+4 x^{5} y^{\prime }+\left (x^{3}+6 x^{2}+4\right ) y&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
79.628 |
|
| 25609 |
\begin{align*}
y+x y^{2}+\left (x -x^{2} y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
79.838 |
|
| 25610 |
\begin{align*}
\left (\operatorname {a4} \,x^{4}+\operatorname {a2} \,x^{2}+\operatorname {a0} \right ) y-2 x \left (-x^{2}+1\right ) y^{\prime }+\left (-x^{2}+1\right )^{2} y^{\prime \prime }&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
80.089 |
|
| 25611 |
\begin{align*}
y^{\prime \prime }+y^{\prime }+y+y^{3}&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
80.112 |
|
| 25612 |
\begin{align*}
\left (y \sqrt {x^{2}+y^{2}}+\left (y^{2}-x^{2}\right ) \sin \left (\alpha \right )-2 x y \cos \left (\alpha \right )\right ) y^{\prime }+x \sqrt {x^{2}+y^{2}}+2 x y \sin \left (\alpha \right )+\left (y^{2}-x^{2}\right ) \cos \left (\alpha \right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
80.169 |
|
| 25613 |
\begin{align*}
x \left (1-2 y x \right ) y^{\prime }+y \left (2 y x +1\right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
80.197 |
|
| 25614 |
\begin{align*}
9 y^{4} \left (x^{2}-1\right ) {y^{\prime }}^{2}-6 x y^{5} y^{\prime }-4 x^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
80.287 |
|
| 25615 |
\begin{align*}
y y^{\prime }+\frac {a \left (5 x +1\right ) y}{2 \sqrt {x}}&=a^{2} \left (-x^{2}+1\right ) \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
80.315 |
|
| 25616 |
\begin{align*}
x y {y^{\prime }}^{2}+\left (x^{22}-y^{2}+a \right ) y^{\prime }-y x&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
80.402 |
|
| 25617 |
\begin{align*}
2 a x +b y+\left (2 c y+b x +e \right ) y^{\prime }&=g \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
80.457 |
|
| 25618 |
\begin{align*}
y^{\prime }&=\frac {2 a x +2 a +x^{3} \sqrt {-y^{2}+4 a x}}{\left (x +1\right ) y} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
80.530 |
|
| 25619 |
\begin{align*}
x^{2} \left (x y^{2}-1\right ) {y^{\prime }}^{2}+2 x^{2} y^{2} \left (-x +y\right ) y^{\prime }-y^{2} \left (x^{2} y-1\right )&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
80.594 |
|
| 25620 |
\begin{align*}
\left (1+{y^{\prime }}^{2}+y y^{\prime \prime }\right )^{2}&=\left (1+{y^{\prime }}^{2}\right )^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
80.633 |
|
| 25621 |
\begin{align*}
y^{\prime }&=\frac {y \left (y x +1\right )}{x \left (-y x +1\right )} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
80.735 |
|
| 25622 |
\begin{align*}
y^{\prime \prime }&=-\frac {\left (2 x^{2}+1\right ) y^{\prime }}{x \left (x^{2}+1\right )}-\frac {\left (-v \left (v +1\right ) x^{2}-n^{2}\right ) y}{x^{2} \left (x^{2}+1\right )} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
80.903 |
|
| 25623 |
\begin{align*}
y^{2}+\left (y x +x^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
80.921 |
|
| 25624 |
\begin{align*}
\left (x^{2}-1\right ) y^{\prime \prime }+2 y^{\prime } x -v \left (v +1\right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
80.994 |
|
| 25625 |
\begin{align*}
y {y^{\prime \prime }}^{3}+y^{3} {y^{\prime }}^{5}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
81.307 |
|
| 25626 |
\begin{align*}
x^{2} y^{\prime \prime }-3 y^{\prime } x +5 y&=x^{2} \sin \left (\ln \left (x \right )\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
81.369 |
|
| 25627 |
\begin{align*}
3 x \left (x^{2}-1\right ) y^{\prime }+x y^{2}-\left (x^{2}+1\right ) y-3 x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
81.384 |
|
| 25628 |
\begin{align*}
3 y-7 x +7+\left (7 y-3 x +3\right ) y^{\prime }&=0 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
81.407 |
|
| 25629 |
\begin{align*}
x^{2}+y^{2}-2 y y^{\prime } x&=0 \\
y \left (1\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
81.458 |
|
| 25630 |
\begin{align*}
\left (c^{2} x^{2}+b^{2}\right ) y-y^{\prime } x +\left (a^{2}-x^{2}\right ) y^{\prime \prime }&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
81.515 |
|
| 25631 |
\begin{align*}
x^{2} y^{\prime }&=y^{2} x^{4}+x^{2 n} f \left (a \,x^{n}+b \right )-\frac {n^{2}}{4}+\frac {1}{4} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
81.559 |
|
| 25632 |
\begin{align*}
x^{2} y^{\prime }&=y^{2} a^{2} x^{2}-y x +b^{2} \ln \left (x \right )^{n} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
81.826 |
|
| 25633 |
\begin{align*}
x^{n +1} y^{\prime }&=x^{2 n} a y^{2}+c \,x^{m}+d \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
81.914 |
|
| 25634 |
\begin{align*}
\left (5+2 x \right )^{2} y^{\prime \prime }-6 \left (5-2 x \right ) y^{\prime }+8 y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
81.977 |
|
| 25635 |
\begin{align*}
10 x -4 y+12-\left (x +5 y+3\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
82.032 |
|
| 25636 |
\begin{align*}
y y^{\prime }-\frac {2 a \left (3 x -10\right ) y}{5 x^{4}}&=\frac {a^{2} \left (x -1\right ) \left (8 x -5\right )}{5 x^{7}} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
82.311 |
|
| 25637 |
\begin{align*}
2 a x +b y+g +\left (2 c y+b x +e \right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
82.549 |
|
| 25638 |
\begin{align*}
\left (x +2 y\right ) {y^{\prime }}^{3}+3 \left (x +y\right ) {y^{\prime }}^{2}+2 y y^{\prime } x&=0 \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
82.906 |
|
| 25639 |
\begin{align*}
\left (x +y+1\right ) y^{\prime }+1+4 x +3 y&=0 \\
y \left (3\right ) &= -4 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
83.039 |
|
| 25640 |
\begin{align*}
-\left (k^{2}-p \left (1+p \right ) \left (-x^{2}+1\right )\right ) y-2 x \left (-x^{2}+1\right ) y^{\prime }+\left (-x^{2}+1\right )^{2} y^{\prime \prime }&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
83.155 |
|
| 25641 |
\begin{align*}
y y^{\prime }-y&=A \left ({\mathrm e}^{\frac {2 x}{A}}-1\right ) \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
83.378 |
|
| 25642 |
\begin{align*}
x^{\prime }&=\frac {2 x}{3 t}+\frac {2 t}{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
83.428 |
|
| 25643 |
\begin{align*}
{y^{\prime }}^{2}+a \,x^{2}+b y&=0 \\
\end{align*} |
✓ |
✗ |
✓ |
✗ |
83.464 |
|
| 25644 |
\begin{align*}
\left (-y+y^{\prime } x \right ) \left (x +y y^{\prime }\right )&=h^{2} y^{\prime } \\
\end{align*} |
✓ |
✗ |
✓ |
✗ |
83.643 |
|
| 25645 |
\begin{align*}
x^{2} y+2 y^{3}-\left (2 x^{3}+3 x y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
83.679 |
|
| 25646 |
\begin{align*}
\left (x +\sqrt {y^{2}-y x}\right ) y^{\prime }-y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
83.751 |
|
| 25647 |
\begin{align*}
3 y-7 x +7+\left (7 y-3 x +3\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
83.866 |
|
| 25648 |
\begin{align*}
\frac {9 t}{5}+2 y+\left (2 t +2 y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
83.889 |
|
| 25649 |
\begin{align*}
x^{\prime }-x+2 y-z&=t^{2} \\
y^{\prime }+3 x-y+4 z&={\mathrm e}^{t} \\
z^{\prime }-2 x+y-z&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
83.896 |
|
| 25650 |
\begin{align*}
y^{\prime }&=\lambda \arccos \left (x \right )^{n} \left (y-a \,x^{m}-b \right )^{2}+a m \,x^{m -1} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
84.066 |
|
| 25651 |
\begin{align*}
3 y-7 x +7+\left (7 y-3 x +3\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
84.092 |
|
| 25652 |
\begin{align*}
9 \sqrt {x}\, y^{{4}/{3}}-12 x^{{1}/{5}} y^{{3}/{2}}+\left (8 x^{{3}/{2}} y^{{1}/{3}}-15 x^{{6}/{5}} \sqrt {y}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
84.210 |
|
| 25653 |
\begin{align*}
{y^{\prime }}^{2} y^{2} \cos \left (a \right )^{2}-2 y^{\prime } x y \sin \left (a \right )^{2}+y^{2}-x^{2} \sin \left (a \right )^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
84.229 |
|
| 25654 |
\begin{align*}
y y^{\prime }-y&=\frac {\left (2 m +1\right ) x}{4 m^{2}}+\frac {A}{x}-\frac {A^{2}}{x^{3}} \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
84.280 |
|
| 25655 |
\begin{align*}
x \left (2 x^{3}+y\right ) y^{\prime }&=6 y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
84.351 |
|
| 25656 |
\begin{align*}
\left (2 x^{{5}/{2}} y^{{3}/{2}}+x^{2} y-x \right ) y^{\prime }-x^{{3}/{2}} y^{{5}/{2}}+x y^{2}-y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
84.365 |
|
| 25657 |
\begin{align*}
\left (x^{2} y-1\right ) y^{\prime }+8 x y^{2}-8&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
84.398 |
|
| 25658 |
\begin{align*}
x \left (-y x +1\right ) y^{\prime }+\left (y x +1\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
84.475 |
|
| 25659 |
\begin{align*}
\left (a \tanh \left (\lambda x \right )+b \right ) y^{\prime }&=y^{2}+c \tanh \left (\mu x \right ) y-d^{2}+c d \tanh \left (\mu x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
84.579 |
|
| 25660 |
\begin{align*}
y+x \left (3 y x -2\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
84.612 |
|
| 25661 |
\begin{align*}
\frac {y^{2}-2 x^{2}}{-x^{3}+x y^{2}}+\frac {\left (2 y^{2}-x^{2}\right ) y^{\prime }}{y^{3}-x^{2} y}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
84.839 |
|
| 25662 |
\begin{align*}
x \left (\left (x^{2}+y^{2}\right )^{{3}/{2}}+2 y^{2}\right )+y \left (\left (x^{2}+y^{2}\right )^{{3}/{2}}-2 x^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
84.863 |
|
| 25663 |
\begin{align*}
y^{\prime }&=\frac {2 x +y-4}{x -y+1} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
84.925 |
|
| 25664 |
\begin{align*}
x \left (2 x^{3}+y\right ) y^{\prime }&=\left (2 x^{3}-y\right ) y \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
85.139 |
|
| 25665 |
\begin{align*}
x^{2} y^{\prime }+y^{2}&=y y^{\prime } x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
85.145 |
|
| 25666 |
\begin{align*}
y^{2}+\left (-x^{3}+y x \right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
85.328 |
|
| 25667 |
\begin{align*}
y^{\prime \prime } x -2 \left (x^{2}-a \right ) y^{\prime }+2 n x y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
85.494 |
|
| 25668 |
\begin{align*}
x y^{2}+y+\left (x^{2} y-x \right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
85.549 |
|
| 25669 |
\begin{align*}
x^{2}-3 y^{2}+2 y y^{\prime } x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
85.837 |
|
| 25670 |
\begin{align*}
p \left (2 k +p \right ) y-\left (1+2 k \right ) x y^{\prime }+\left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
85.859 |
|
| 25671 |
\begin{align*}
y y^{\prime }-y&=-\frac {6}{25} x -A \,x^{2} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
85.864 |
|
| 25672 |
\begin{align*}
x^{2} \left (x +1\right ) y^{\prime \prime }+x \left (4 x +3\right ) y^{\prime }-y&=x +\frac {1}{x} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
85.936 |
|
| 25673 |
\begin{align*}
x \left (3-y x \right ) y^{\prime }&=y \left (y x -1\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
85.954 |
|
| 25674 |
\begin{align*}
y^{\prime }&=x^{2}-y^{2} \\
y \left (0\right ) &= 2 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
86.093 |
|
| 25675 |
\begin{align*}
a x y-b +\left (c x y-d \right ) x y^{\prime }&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
86.265 |
|
| 25676 |
\begin{align*}
\frac {1}{\sqrt {x^{2}+y^{2}}}+\left (\frac {1}{y}-\frac {x}{y \sqrt {x^{2}+y^{2}}}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
86.335 |
|
| 25677 |
\begin{align*}
x^{\prime }&=a x+g y+\beta z \\
y^{\prime }&=g x+b y+\alpha z \\
z^{\prime }&=\beta x+\alpha y+c z \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
86.938 |
|
| 25678 |
\begin{align*}
\left (\sinh \left (\lambda x \right ) a +b \right ) y^{\prime }&=y^{2}+c \sinh \left (\mu x \right ) y-d^{2}+c d \sinh \left (\mu x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
87.025 |
|
| 25679 |
\begin{align*}
\left (19+9 x +2 y\right ) y^{\prime }+18-2 x -6 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
87.551 |
|
| 25680 |
\begin{align*}
y \left (\operatorname {a2} +\operatorname {b2} \,x^{k}+\operatorname {c2} \,x^{2 k}+\left (-1+\operatorname {a1} +\operatorname {b1} \,x^{k}\right ) f \left (x \right )+f \left (x \right )^{2}+f^{\prime }\left (x \right )\right )+x \left (\operatorname {a1} +\operatorname {b1} \,x^{k}+2 f \left (x \right )\right ) y^{\prime }+x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
87.694 |
|
| 25681 |
\begin{align*}
x x^{\prime }+t^{2} x&=\sin \left (t \right ) \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
87.843 |
|
| 25682 |
\begin{align*}
x^{2} {y^{\prime }}^{2}+\left (2 x -y\right ) y y^{\prime }+y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
87.885 |
|
| 25683 |
\begin{align*}
y^{\prime }&=\frac {x^{{5}/{3}}}{y+x^{{4}/{3}}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
87.902 |
|
| 25684 |
\begin{align*}
2 x \left (x -1\right ) y^{\prime \prime }+\left (2 x -1\right ) y^{\prime }+\left (a x +b \right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
88.241 |
|
| 25685 |
\begin{align*}
2 \left (a \,x^{3}+b \,x^{2}+c x +d \right ) y^{\prime \prime }+\left (3 a \,x^{2}+2 b x +c \right ) y^{\prime }+\lambda y&=0 \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
88.276 |
|
| 25686 |
\begin{align*}
y^{\prime } x&=a \tan \left (\lambda x \right )^{m} y^{2}+k y+a \,b^{2} x^{2 k} \tan \left (\lambda x \right )^{m} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
88.279 |
|
| 25687 |
\begin{align*}
\left (x +y\right )^{2} y^{\prime }&=a^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
88.289 |
|
| 25688 |
\begin{align*}
y^{2}&=\left (x^{2}+2 y x \right ) y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
88.298 |
|
| 25689 |
\begin{align*}
y^{\prime \prime }&=-\frac {2 x y^{\prime }}{x^{2}-1}-\frac {\left (-a^{2} \left (x^{2}-1\right )^{2}-n \left (n +1\right ) \left (x^{2}-1\right )-m^{2}\right ) y}{\left (x^{2}-1\right )^{2}} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
88.433 |
|
| 25690 |
\begin{align*}
y^{\prime }&=f \left (x \right ) y^{2}-a \tan \left (\lambda x \right )^{2} \left (a f \left (x \right )-\lambda \right )+a \lambda \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
88.500 |
|
| 25691 |
\begin{align*}
p \left (1+2 k +p \right ) y-2 \left (1+k \right ) x y^{\prime }+\left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
88.786 |
|
| 25692 |
\begin{align*}
\operatorname {a2} x y+\left (\operatorname {b1} \,x^{2}+\operatorname {a1} \right ) y^{\prime }+x^{3} y^{\prime \prime }&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
88.924 |
|
| 25693 |
\begin{align*}
2 x \sin \left (\frac {y}{x}\right )+2 x \tan \left (\frac {y}{x}\right )-y \cos \left (\frac {y}{x}\right )-y \sec \left (\frac {y}{x}\right )^{2}+\left (x \cos \left (\frac {y}{x}\right )+x \sec \left (\frac {y}{x}\right )^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
89.398 |
|
| 25694 |
\begin{align*}
\left (a \,x^{n}+x^{m} b +c \right ) y^{\prime }&=a \,x^{-2+n} y^{2}+b \,x^{m -1} y+c \\
\end{align*} |
✓ |
✗ |
✗ |
✗ |
89.496 |
|
| 25695 |
\begin{align*}
y&=2 x +y^{\prime }-\frac {{y^{\prime }}^{3}}{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
89.536 |
|
| 25696 |
\begin{align*}
a_{1} x +k y+c_{1} +\left (k x +b_{2} y+c_{2} \right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
89.697 |
|
| 25697 |
\begin{align*}
\sin \left (2 x \right )^{n +1} y^{\prime }&=a y^{2} \sin \left (x \right )^{2 n}+b \cos \left (x \right )^{2 n} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
89.804 |
|
| 25698 |
\begin{align*}
\left (a {y^{\prime }}^{2}-b \right ) x y+\left (b \,x^{2}-a y^{2}+c \right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✗ |
✓ |
✗ |
90.014 |
|
| 25699 |
\begin{align*}
x^{n} y^{\prime }&=a^{2} x^{2 n -2}+b^{2} y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
90.052 |
|
| 25700 |
\begin{align*}
x \left (x^{3}+y\right ) y^{\prime }&=\left (x^{3}-y\right ) y \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
90.165 |
|